Faculty of Mathematics, Physics
and Informatics
Comenius University in Bratislava

Seminar on Qualitative Theory of Differential Equations - Pavol Bokes (3.12.2020)

Thursday 3.12.2020 at 14:00, online

30. 11. 2020 12.38 hod.
By: Pavol Quittner

Pavol Bokes:
Effects of large distributed delays on noisy genetic feedback circuits

MS Teams

Bursty protein production is an important source of stochastic noise in the expression of individual genes. In the first part of the talk, we will review basic Markovian models of non-bursty and bursty gene expression. We will emphasise that the non-bursty model admits Poissonian protein distributions, whereas the bursty model generates super-Poissonian noise in protein level. We will argue that extending a bursty model with a large distributed production delay buffers the super-Poissonian protein noise down to Poissonian levels. In the second part of the talk, the delayed bursty production model will be extended by feedback in burst frequency and analysed with Wentzel--Kramers--Brillouin (WKB)/large-deviation-theory (LDT) methods. An ordinary differential equation will be formulated that captures the model's limiting deterministic behaviour; the equation will be extended by an additional dimension into a planar Hamiltonian system that characterises stochastically-driven transitions between deterministic equilibria. In the presence of multiple equilibria, the protein distribution will be approximated by a mixture of Poisson modes; the WKB/LDT analysis thereby quantifies the mixture weights. quittner Posts: 108 Joined: Fri Oct 12, 2012 11:21 am

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